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Popular >

integral from 1 to e of (x+2)/x

Solution

\int_{1}^{e} \frac{x + 2}{x} d x

Solution

e + 1

+1

Decimal Notation

3.71828 \dots

Solution steps

\int_{1}^{e} \frac{x + 2}{x} d x

Expand

\frac{x + 2}{x} : 1 + \frac{2}{x}

= \int_{1}^{e} 1 + \frac{2}{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{e} 1 d x + \int_{1}^{e} \frac{2}{x} d x

\int_{1}^{e} 1 d x = e - 1

\int_{1}^{e} \frac{2}{x} d x = 2

= e - 1 + 2

Simplify

= e + 1

Popular Examples

integral from 0 to 5/9 of 1/(81x^2+25)

\int_{0}^{\frac{5}{9}} \frac{1}{81 x ^{2} + 25} d x

integral from 0 to 2pi of sin(3x)cos(4x)

\int_{0}^{2 π} sin (3 x) cos (4 x) d x

integral from 1 to e of ((ln(x))^3)/x

\int_{1}^{e} \frac{( ln ( x ) ) ^{3}}{x} d x

integral from 0 to pi of (2x-1)cos(5x)

\int_{0}^{π} (2 x - 1) cos (5 x) d x

integral from 2 to 3 of 1/(2x^2+3x-2)

\int_{2}^{3} \frac{1}{2 x ^{2} + 3 x - 2} d x

Frequently Asked Questions (FAQ)

What is the integral from 1 to e of (x+2)/x ?
The integral from 1 to e of (x+2)/x is e+1